I don't know the intention of the screen writers, but the simple present would make it sound like a formal proverb - kind of preachy. The continuous is more informal and colloquial. It also gives the impression that this happens around us all the time, almost magically.
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kane159Everything is happening for a reason.All the things that are now happening to us are happening for a reason. (It's specific to things happening within a specific context, in this case, the things happening to and around the characters in the TV series.)